366 The Representation of Oceanic Movements and Kinematics 



azimuth of each isogen so that the chart is covered complete with short dashes. It is 

 then easy to draw in the curves tangential to these short dashes and these curves are 

 the stream lines. Werenskjold (1922) has pointed out that it is possible to draw in 

 a number of isogons rather quickly by simply using two charts of the eastern and 

 northern components of the current u and v. If a is the azimuth of the current then 



V 



tan a = - = k. 

 u 



Each isogon is fixed by ^ = const. Two isogons can thus be drawn in immediately: 

 for A: = and k = co; they correspond to lines y = and m = 0. Their intersections 

 give the singular points through which all isogons must pass. Since the relation 



V — ku = 



is satisfied only at points where m = y = for all values of k. Further isogons are 

 easily found; they can be limited to the eight isogons where ^ = 0, ij, ±1 and ±2; 

 corresponding to these are the azimuths 0°, 26|°, 45°, 63|°, 90° and so on. These 

 usually fix the current field with sufficient accuracy. 

 The stream lines are given by integrations of the differential equation 



— = A: = ^ 

 dx u 



(see equation (X. 22) on p. 323). If v and u are given as analytical functions of the co- 

 ordinates X and y, then in many cases an accurate integration of the equation, and 

 therefore also a representation, of the current field is possible. Werenskjold has given 

 a large number of cases of this type and has discussed them in detail. Reference is 

 made to these. Of particular interest are those cases where complex singularities 

 occur; to draw these complicated patterns is usually rather tiresome, but mathematically 

 they are no more difficult than the simple ones. An example will illustrate this. If u 

 and V are given by 



— u = x^ + (y + ay — r^, 



V = x^ + (>' — ay + r^, 



where r^ > a^, then the integration of the diff'erential equation above gives the stream 

 lines represented in Fig. 155a; the isogons u = and v = are circles which are shown 

 by dotted lines in the figure. Their points of intersection give the singular points, one 

 of which is a neutral point and the other is a convergence point ; they are connected 

 by a line of convergence. Such connections of the singularities are relatively frequent 

 in stream-line patterns of ocean currents. 



(d) Examples of Current Charts 



Current charts based on these principles have been prepared for many parts of the 

 ocean, usually for mean conditions since there are almost no synoptic data available. 

 They show only surface currents. Various types of presentation have been used. An 

 accurate representation based on strict hydrodynamic principles has been introduced 

 by Bjerknes. Analysis of the current fields and their resolution along the extended 

 lines of convergence and divergence, with more or numerous complex singularities, 

 has shown that the previous conception of large horizontal circulating systems in the 



